简化英文运筹案例.docVIP

一、LP 1. Example 2.3-1 (Urban Renewal Model) The city of Erstville is faced with a severe budget shortage. Seeking a long-term solution, the city council votes to improve the tax base by condemning an inner-city housing area and replacing it with a modern development. The project involves two phases: (1) demolishing substandard houses to provide land for the new development, and (2) building the new development. The following is a summary of the situation. As many as 300 substandard houses can be demolished. Each house occupies a .25-acre lot. The cost of demolishing a condemned house is $2000. Lot sizes for new single-, double-, triple-, and quadruple-family homes( units) are .18, .28, .4, and .5 acre, respectively. Streets, open space, and utility easements account for 15% of available acreage. In the new development the triple and quadruple unites account for at least 25% of the total. Single units must be at least 20% of all units and double units at least 10%. The tax levied per unit for single, double, triple, and quadruple units is $1000, $1900, $2700 , and $3400, respectively. The construction cost per unit for single-, double-, triple-, and quadruple- family homes is $50,000, $70,000, $130,000, and $160,000, respectively. Financing through a local bank can amount to a maximum of $15 million. How many units of each type should be constructed to maximize tax collection? Mathematical model: x1=Number of units of single-family homes x2=Number of units of double-family homes x3=Number of units of triple-family homes x4=Number of units of quadruple-family homes x5=Number of old homes to be demonished The complete model thus becomes Max z=1000x1+1900x2+2700x3+3400x4 Subject to .18x1+.28x2+.4x3+.5x4-.2125x5 x5 Solution: Total tax collection =z= $343,965 Number of single homes =x1=35.8336 units Number of double homes =x2=98.5399 units Number of triple homes =x3=44.7945 units Number of quadruple homes =x4=0 units Number of homes demonished =x5=